Kaplunovsky - hw 01

homework 01 Due: Jan 26 2007, 4:00 am 1 Question 1, chap 1, sect 5. part 1 of 3 5 points A solid aluminum cube has sides each of length L. A second cube of the same material has sides three times the length of the first cube, i.e. , 3 L. Compared to the first cube, the density of the second cube is 1. four times as much as the first cube. 2. the same as the first cube. correct 3. twenty-four times as much as the first cube. 4. sixteen times as much as the first cube. 5. two times as much as the first cube. 6. eight times as much as the first cube. 7. nine times as much as the first cube. 8. twenty-seven times as much as the first cube. 9. None of these 10. sixty-four times as much as the first cube. Explanation: Density is defined as mass per unit volume and therefore is a property of the material, in this case aluminum, not the shape or size and so remains the same. Question 2, chap 1, sect 5. part 2 of 3 5 points Compared to the first cube, the weight of the second cube is 1. twenty-seven times as much as the first cube. correct 2. sixty-four times as much as the first cube. 3. the same as the first cube. 4. two times as much as the first cube. 5. four times as much as the first cube. 6. eight times as much as the first cube. 7. nine times as much as the first cube. 8. None of these 9. sixteen times as much as the first cube. 10. twenty-four times as much as the first cube. Explanation: The first cube has a volume of V 1 = L L L = L 3 . The second cube has a volume of V 2 = 3 L 3 L 3 L = (3 L ) 3 = 27 L 3 . The ratio of the surface areas is V 2 V 1 = 27 L 3 L 3 = 27 . The second cube has 27 times the volume of the first cube and so 27 times the mass because the density is defined as mass per unit volume. The second cube has 27 times the weight because it has 27 times the mass. Question 3, chap 1, sect 5. part 3 of 3 5 points Compared to the first cube, the total sur- face area of the second cube is 1. twenty-four times as much as the first cube. 2. nine times as much as the first cube. correct 3. sixteen times as much as the first cube. homework 01 Due: Jan 26 2007, 4:00 am 2 4. the same as the first cube. 5. twenty-seven times as much as the first cube. 6. eight times as much as the first cube. 7. sixty-four times as much as the first cube. 8. four times as much as the first cube. 9. None of these 10. ninty-six times as much as the first cube. Explanation: The surface of one side of the first cube is A 1 = L L = L 2 . Every cube has 6 sides so the total surface area of the first cube is A 1 = 6 L 2 . The surface area of one side of the second cube is A 2 = 3 L 3 L = 9 L 2 . So the total surface area of the second cube is A 2 = 6 9 L 2 = 54 L 2 ....
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